When the mayor of Madrid, Ana Botella, inaugurated Plaza Margaret Thatcher in 2014, flanked by the former British prime minister’s son Mark and his wife, it sparked a series of rows about the appropriateness of having a city square named after the “Iron Lady”.

Over the following days and months, the sign bearing Thatcher’s name was repeatedly vandalised, with Madrid-based British socialists campaigning to have the square renamed Jack Jones Plaza, after the Transport and General Workers’ Union head who fought with the International Brigades.

While Carmena’s office issued a denial, and Plaza Margaret Thatcher still stands in Madrid, the mayor has now set her sights on street names associated with former dictator General Francisco Franco. Policies such as ordering Balthazar in the annual Three Kings parade be played by a black man rather than a white man blacked up, or opening the elite Club de Campo Villa de Madrid to the public, have proved controversial in some quarters, but it is the idea of changing Franco-era street names that has arguably gone deeper and reopened old divisions.

A worker removes the sign for General Franco Street on Gran Canaria in 2006. Photograph: Jose Carlos Guerra/EPA

While many streets and squares directly bearing the name of Franco were renamed a decade ago under socialist prime minister José Luis Zapatero’s Historical Memory law, Carmena believes the Popular party of Botella never went far enough in the two and a half decades it ruled Madrid until her surprise victory last June.

Many indirect references remain to Franco, who ruled from the end of the three-year bloody civil war in 1939 to his death in 1975. Carmena has announced 30 names that are to be changed, including Plaza de Arriba España near Real Madrid’s Bernabéu stadium – named after a Franco salute meaning “Onwards Spain!” – and the Calle de los Caídos de la División Azul, which commemorates the Spanish army’s Blue Division that fought with the Germans during the second world war. Another – Calle General Yague – is named after one of Franco’s officers, known as the Butcher of Badajoz for overseeing the massacre of hundreds of civilians.

Replacement names are still under discussion, but local reports say one street is set to be renamed after Melchor Rodríguez García, an anarchist known as Él Ángel Rojo (the Red Angel), the last mayor of Madrid before Franco’s forces took over the city. Carmena’s administration has called for a more “pluralistic, democratic and diverse” face for the city streets, with more named after women and victims of terror.

Amid fierce resistance from some quarters, however, none of the street name changes first floated 12 months ago have yet been made, and the mayor recently set up a commission in the hope of achieving consensus.

Bobby Sands Street in Tehran, named after the IRA prisoner who died following a hunger strike in the Maze prison. Photograph: Behrouz Mehri/AFP/Getty Images

It’s not only in Madrid where name changing is a big issue. In Poland, around 1,500 streets, squares and bridges could have their names revised in an effort by the ruling Law and Justice party to “de-communise” the country.

Polish cities and towns changed the most blatant communist-inspired names after the rejection of soviet power in 1989, but critics say many survive. The move risks a row with Russia – sensitive to anything which could remove “monuments of gratitude to the Red Army” – and has angered the Polish left, who fear second world war communist resistance fighters could be erased from visible history.

Other mooted name changes are designed to send a political message to a foreign power. Recent reports suggest the Tehran road housing the Saudi Arabian embassy could be renamed Sheikh Nimr al-Nimr Street, after a Shia cleric executed by the Saudis. It wouldn’t be the first time Iran has used the technique: in 1981 Churchill Street, where the British embassy was based, was renamed Bobby Sands Street after the IRA member who died on hunger strike in the Maze prison. The embassy skirted the problem by knocking through to a new entrance on a street named after Persian poet Ferdowsi, an Iranian hero and so safe from future change.

The US has employed similar tactics. In 1984, the segment of Washington DC’s 16th Street where the Soviet embassy was based was renamed Andrei Sakharov Plaza, after the Nobel-prize winning nuclear physicist and jailed Soviet dissident. And in 2014, the US Congress voted to rename the Washington Street where the Chinese embassy is located Liu Xiaobo Plaza, after the Nobel Peace laureate imprisoned in China. If the Senate had not blocked the move, Beijing might have followed through with reported threats to rename the road where the US embassy is based Snowden Street.

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But apart from confusing Google Maps and taxi drivers – and the cost to businesses of reprinting letterheads and business cards – what are the wider implications of name changing for the character of a city?

Darran Anderson, author of Imaginary Cities, says that much of our sense of identity and belief is wrapped up in signs and symbols. “Once you decide to name a street after a person or an event, rather than topography, you’ve started something intrinsically political and subjective,” he says. “When we fail to look at what existed previously and why, we rob ourselves of context and roots.”

While Anderson would be happy to see the removal of Franco-era signs, he stresses the importance of not burying or denying the past. “Any psychologist will tell you this is a very unwise proposition, and that works for nations as well as individuals. Change is welcome by all means, but an understanding of why it was necessary and what came before is also essential.

“Our lives and the lives of our cities operate in time as well as space, and it’s important to acknowledge that. We are who we are because, and in spite, of where we’ve come from.”